On the optimisation of methods for the computation of many-beam structure images

The necessity to calculate structure images for the interpretation of high-resolution electron micrographs has often been emphasized However, when large unit cells and/or heavy atoms are involved, the number of beams used for the calculations has to be increased to the order of 1000-10000, whereas an accurate simulation of the beam divergence drastically augments the computing time [11], For these reasons the computational techniques used hitherto, require fairly high computer facilities. On the other hand because of the availability of mini laboratory computers [≤32k words] in most laboratories nowadays, an image calculation program that could be performed on such a computer with sufficient speed to allow direct feedback, would be very welcome. We searched in this work for optimal computational techniques that meet these requirements without loss of generality. The investigation was carried out in four distinct steps. 1. Basic expression It was previously shown [5,6] that, when backscattered electrons are neglected, which is a valid assumption [7], all the existing dynamical diffraction formulations can be reduced to a formal expression for Φ[z], the vector of the diffraction amplitudes as a function of the crystal depth: with the boundary condition Φ(o) = T represents the diagonal propagation matrix with components T, where s is the excitation error.